With the election 25 days away, Mayor Thomas M. Menino huddled in Dorchester with more than a dozen of the city’s building and trades union leaders Saturday to figure out how to persuade voters — including many in organized labor — to cast their ballot for Elizabeth Warren for US Senate.

Martin F. Walsh, business manager of Laborers Local 223, said he has talked to union members such as teachers, police officers, and electricians who insist on voting for the Republican incumbent, Scott Brown.

Walsh, 57, cautioned the leaders to make sure they talk to members of their own families about the race.

“There isn’t a person around this table, I don’t care who he is, who doesn’t have a relative voting for Scott Brown,” he said. “My sister-in-law has a Scott Brown sticker on her fridge.”

Walsh’s cousin, state Representative Martin J. Walsh — both men were named after their grandfather — said in an interview after the meeting that there is a misperception that the rank and file vote in lockstep when unions announce support for a candidate.

“Our unions are made up of the average voter on the street and we have to go out and explain to them and market Elizabeth Warren, or any other candidate,” said Representative Walsh, who is also general agent of the Building and Construction Trades Council of the Metropolitan District. “Our workers have their own views.”

‘There isn’t a person around this table, I don’t care who he is, who doesn’t have a relative voting for Scott Brown.’

In 2010, after Brown defeated Democrat Martha Coakley in the special election, a poll found that 49 percent of union voters chose the Republican. In September, 46 percent of 132 union members said they supported Brown while 41 percent supported Warren, according to a Suffolk University/WHDH Channel 7 poll.

Menino called the meeting on Thursday, marking the first time in recent memory that union leaders gathered with the city’s mayor to discuss campaign strategy. The gathering underscored the urgency many of them feel about the outcome of the tight Senate race between Warren and Brown.

“It’s not about being the best retail politician,” Menino said during the meeting, where he sat at the head of a long table in the conference room of the International Brotherhood of Electrical Workers Local 103 office. “How do we get the message to get down and dirty to all our members? It’s not about a beauty contest. It’s about electing who will be with us to create jobs for the construction trades . . . How do we motivate our guys?”

The union leaders represent a variety of laborers, including pipefitters, sheetmetal workers, and painters. They said they have 75,000 members in Boston who could be the key to bringing victory to Warren if they canvass the city and turn out to vote.

On Saturday, about 700 union workers rallied at an event organized by the AFL-CIO in Malden before spreading out to cities and towns in Middlesex County to stump for Warren.

Representative Walsh said more than 100 members from Laborers Local 223 are planning to meet in Dorchester on Sunday, then fan out to Hyde Park, Allston-Brighton, and Charlestown.

“I’ve never seen such a coordinated effort for any campaign,” he said. “I’m feeling energy here.”

At the meeting, a Menino aide stressed that members should call other members directly, and also reach out to other people in the household who are eligible to vote. Throughout the meeting, union leaders said they are stressing to members and others Brown’s votes against several jobs bills; his opposition to an earmark in the defense budget that helped fund a program connecting war veterans to the construction field; and his decision to hold up extensions to unemployment insurance to extract concessions on other issues, such as tax cuts. Menino, whose get-out-the-vote machine could be crucial to Warren’s chances, told the leaders to meet weekly, for an hour, to gauge how their efforts are going.

Brown’s campaign said he has received the endorsement of various police organizations, including the Boston Police Superior Officers Federation, the Worcester Police Patrolmen’s Union, and the unions representing patrol officers and sergeants from the MBTA. On Saturday, he picked up the support of the Lowell Police Patrolmen’s Association.

The Brown campaign said union workers’ support of Warren should be viewed skeptically, pointing to an online video that shows a carpenters union member telling a Republican tracker that he would be fined $250 if he did not attend.

“This type of behavior is disgraceful, and Warren should immediately condemn these tactics and apologize to union members who have been compelled by their leadership to support her against their will,” said Brown spokeswoman Alleigh Marré.

Mark Erlich, executive secretary treasurer of the New England Regional Council of Carpenters, said the worker was describing an annual assessment that is waived when members do community service, which can include attending a political rally.

“Brown is flat-out wrong,” Erlich said. “We have never and never will fine any member for not participating in political activity and have never paid any member to participate. Brown’s voting record is motivation enough.”

The Warren campaign e-mailed the Globe photos of the candidate and labor leaders speaking at the rally in Malden.

“Elizabeth is proud of the support she has from working men and women across this state, and their growing enthusiasm for her candidacy,” campaign spokeswoman Alethea Harney said. “This morning’s rally demonstrates both.”